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A097711 Column 1 of triangle A097710, in which row (n) is formed from the sums of the adjacent terms in row (n-1) of the matrix square of A097710.

%I A097711 #8 Feb 22 2024 02:20:57
%S A097711 1,3,13,88,951,16691,484490,23701698,1990327810,291750344191,
%T A097711 75757923092106,35286335933354828,29791358931890967248,
%U A097711 45989706937220594708463,130760311958838053647976497
%N A097711 Column 1 of triangle A097710, in which row (n) is formed from the sums of the adjacent terms in row (n-1) of the matrix square of A097710.
%C A097711 Related to the number of tournament sequences (A008934).
%H A097711 G. C. Greubel, <a href="/A097711/b097711.txt">Table of n, a(n) for n = 0..84</a>
%t A097711 T[n_, k_]:= T[n, k]= If[n<0 || k>n, 0, If[n==k, 1, If[k==0, Sum[T[n-1, j]*T[j,0], {j,0,n-1}], Sum[T[n-1,j]*(T[j,k-1] +T[j,k]), {j,0,n-1}] ]]]; (* T = A097710 *)
%t A097711 A097711[n_]:= T[n+1,1];
%t A097711 Table[A097711[n], {n,0,30}] (* _G. C. Greubel_, Feb 21 2024 *)
%o A097711 (SageMath)
%o A097711 @CachedFunction
%o A097711 def T(n, k): # T = A097710
%o A097711     if n< 0 or k<0 or k>n: return 0
%o A097711     elif k==n: return 1
%o A097711     elif k==0: return sum(T(n-1,j)*T(j,0) for j in range(n))
%o A097711     else: return sum(T(n-1, j)*(T(j, k-1)+T(j,k)) for j in range(n))
%o A097711 def A097711(n): return T(n+1,1)
%o A097711 [A097711(n) for n in range(31)] # _G. C. Greubel_, Feb 21 2024
%Y A097711 Cf. A008934, A097710.
%K A097711 nonn
%O A097711 0,2
%A A097711 _Paul D. Hanna_, Aug 22 2004